Effects of circular plates on forced vibration of orthogonally stiffened cylindrical shell in wavenumber-frequency domain

Abstract

A modified variational method for orthogonally stiffened cylindrical shell coupled with multiple circular plates is proposed in this paper. A unified variational modelling procedure is developed to accommodate three dimensional deformation restrains between the shell and substructures, including circular plates, ring and axial stiffeners. The vibration displacements are analytically expanded with Fourier series in the circumferential direction. The input energies due to external loads and the responses of the shell in circumferential wavenumber domain can be naturally obtained, which significantly facilitate the effect analysis of substructures. Close orthogonal independent polynomials are employed for the displacements in the axial direction to achieve satisfactory solutions. The convergence and accuracy of the present method are validated by comparing the analytical and numerical results. The effects of circular plates on vibration responses under different external forces are investigated. The contributions of different circumferential modes to the forced responses are analyzed, and reasons for the effects of the circular plates are then revealed in the circumferential wavenumber-frequency domain. The results indicate that the circular plates not only lead to frequency shift, but also coupling of the circumferential modes of the shell, which will respectively account for frequency shifts and increase of the resonance peaks.